Preheat the oven to 375 degrees F.
Using a small ring mold just a little bit larger than the size of the figs, cut the pastry into 40 individual portions. Line up the puff pastry pieces on a baking sheet.
Slice off the base end of the figs. Arrange a fig base in the center of each puff pastry round and reserve the remaining fig tops. In a small bowl, beat the eggs with a fork to make an egg wash. Brush the pastry with the egg wash and sprinkle with 1 tablespoon of the sugar. Bake until the puff pastry is crisp and golden brown, approximately 10 to 12 minutes. Remove the tarts from the oven and immediately put a teaspoon of goat cheese into the center of each tart to soften.
Remove the stems from the fig tops. Cut the figs and strawberries into small slices, put them into a medium saucepan, and sprinkle with the remaining tablespoon of sugar. Cut the vanilla bean in half lengthwise. Using the back of a paring knife, scrape the seeds out of each half of the vanilla bean and add the seeds and the vanilla bean to the fig and strawberry mixture. Add the vinegar and clove. Put the pan over medium-low heat and cook until the fruit is warmed through. Remove the vanilla bean and discard.
Arrange the tarts on serving platters and spoon a small amount of warm fruit compote over each tart. Garnish with micro greens and serve.